Finite Group Databasebeta

← C137×#23482 #46872868

Subgroups — C137×#23482 #46872868

Order 35072.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C137C211yesmaximal, characteristic
2C2×#428×C137C211yesmaximal, characteristic, complemented
3C2×#417×C137C211yesmaximal, characteristic, complemented
4C2×#417×C137C211yesmaximal, characteristic, complemented
5C2×#407×C137C211yesmaximal, characteristic, complemented
6C2×#380×C137C211yesmaximal, characteristic, complemented
7#2036×C137C212yesmaximal, complemented
8#2035×C137C212yesmaximal, complemented
9#2034×C137C212yesmaximal, complemented
10#2033×C137C212yesmaximal, complemented
11#1736×C137C211yesmaximal, characteristic, complemented
12C22×#41×C137C2211yescharacteristic
13C24×C4×C137C2211yescharacteristic
14C22×M16×C137C2211yescharacteristic
15C22×M16×C137C2211yescharacteristic
16#525×C137—24no—
17#525×C137—24no—
18C2×#123×C137—21no—
19C2×C22⋊Q8×C137C2211yescharacteristic
20C2×C22⋊Q8×C137C2211yescharacteristic
21C2×#121×C137C2211yescharacteristic
22C2×#121×C137C2211yescharacteristic
23C2×#120×C137—21no—
24C2×C4×D4×C137—21no—
25C2×C4×D4×C137—21no—
26C2×#117×C137C2211yescharacteristic
27C22×C4⋊C4×C137C2211yescharacteristic
28C22×C4⋊C4×C137C2211yescharacteristic
29C22×C22⋊C4×C137—21no—
30#428×C137—24no—
31C2×#107×C137C2212yescomplemented
32C2×#106×C137C2212yescomplemented
33#417×C137—24no—
34#417×C137—24no—
35C2×#103×C137C2212yescomplemented
36C2×#103×C137C2212yescomplemented
37C2×#102×C137C2212yescomplemented
38C2×#102×C137C2212yescomplemented
39#407×C137—24no—
40C2×C22⋊C8×C137C2212yes—
41C2×C22⋊C8×C137C2212yes—
42#380×C137—21no—
43#380×C137—21no—
44#380×C137C2212yes—
45#380×C137C2212yes—
46C2×#95×C137—21no—
47#340×C137C2212yescomplemented
48#340×C137C2212yescomplemented
49C25×C137D411yescharacteristic
50C2×#41×C137—22no—
51C2×#41×C137—22no—
52C2×#41×C137—22no—
53C2×#41×C137—22no—
54C2×#41×C137—22no—
55C2×#41×C137D414yes—
56C22×Q8×C137C2311yescharacteristic
57C22×D4×C137—21no—
58C22×D4×C137—21no—
59C22×D4×C137—21no—
60C22×D4×C137C2311yescharacteristic
61C23×C4×C137—22no—
62C23×C4×C137—21no—
63C23×C4×C137—22no—
64C23×C4×C137—22no—
65C23×C4×C137—22no—
66C23×C4×C137—22no—
67C23×C4×C137—22no—
68C23×C4×C137—21no—
69C23×C4×C137—21no—
70C23×C4×C137D411yescharacteristic
71C23×C4×C137D411yescharacteristic
72C23×C4×C137D411yescharacteristic
73C23×C4×C137C2311yescharacteristic
74C23×C4×C137C2311yescharacteristic
75C23×C4×C137C2311yescharacteristic
76C2×M16×C137—22no—
77C2×M16×C137—22no—
78C2×M16×C137—22no—
79C2×M16×C137—22no—
80C2×M16×C137—22no—
81C2×M16×C137D414yescomplemented
82C22×C8×C137C2312yes—
83C22×C8×C137C2312yes—
84#123×C137—28no—
85C22⋊Q8×C137—22no—
86C22⋊Q8×C137—22no—
87C22⋊Q8×C137—22no—
88C22⋊Q8×C137—22no—
89#121×C137—22no—
90#121×C137—22no—
91#121×C137—22no—
92#121×C137—22no—
93#120×C137—28no—
94C4×D4×C137—28no—
95C4×D4×C137—28no—
96#117×C137—22no—
97#117×C137D414yes—
98C2×C4⋊C4×C137—21no—
99C2×C4⋊C4×C137—21no—
100C2×C4⋊C4×C137—22no—
101C2×C4⋊C4×C137—22no—
102C2×C4⋊C4×C137—22no—
103C2×C4⋊C4×C137—22no—
104C2×C4⋊C4×C137—21no—
105C2×C4⋊C4×C137—21no—
106C2×C4⋊C4×C137C2312yes—
107C2×C4⋊C4×C137C2312yes—
108C2×C4⋊C4×C137C2311yescharacteristic
109C2×C4⋊C4×C137C2311yescharacteristic
110C2×C22⋊C4×C137—21no—
111C2×C22⋊C4×C137—21no—
112C2×C22⋊C4×C137—21no—
113C2×C22⋊C4×C137—21no—
114C2×C22⋊C4×C137—21no—
115C2×C22⋊C4×C137—22no—
116C2×C22⋊C4×C137—22no—
117C2×C22⋊C4×C137—44no—
118C2×C42×C137—21no—
119#107×C137—24no—
120#106×C137—24no—
121#103×C137—24no—
122#103×C137—24no—
123#102×C137—24no—
124#102×C137—24no—
125C22⋊C8×C137—24no—
126C22⋊C8×C137—24no—
127#95×C137—22no—
128#95×C137—22no—
129C24×C137—22no—
130C24×C137—22no—
131C24×C137—22no—
132C24×C137—22no—
133C24×C137—22no—
134C24×C137—21no—
135C24×C137—41no—
136C24×C137—41no—
137C24×C137C2×D411yescharacteristic
138C24×C137C2×D411yescharacteristic
139C24×C137C2×D411yescharacteristic
140#41×C137—28no—
141#41×C137—28no—
142#41×C137—44no—
143#41×C137—44no—
144C2×Q8×C137—21no—
145C2×Q8×C137—21no—
146C2×Q8×C137—21no—
147C2×Q8×C137—21no—
148C2×Q8×C137—21no—
149C2×Q8×C137C2×D412yes—
150C2×D4×C137—24no—
151C2×D4×C137—24no—
152C2×D4×C137—24no—
153C2×D4×C137—21no—
154C2×D4×C137—21no—
155C2×D4×C137—21no—
156C2×D4×C137—21no—
157C2×D4×C137—21no—
158C2×D4×C137—42no—
159C2×D4×C137—42no—
160C2×D4×C137—42no—
161C2×D4×C137—42no—
162C2×D4×C137—42no—
163C2×D4×C137—42no—
164C2×D4×C137C2×D412yes—
165C22×C4×C137—22no—
166C22×C4×C137—22no—
167C22×C4×C137—22no—
168C22×C4×C137—21no—
169C22×C4×C137—21no—
170C22×C4×C137—21no—
171C22×C4×C137—22no—
172C22×C4×C137—22no—
173C22×C4×C137—24no—
174C22×C4×C137—22no—
175C22×C4×C137—22no—
176C22×C4×C137—22no—
177C22×C4×C137—22no—
178C22×C4×C137—21no—
179C22×C4×C137—21no—
180C22×C4×C137—21no—
181C22×C4×C137—21no—
182C22×C4×C137—21no—
183C22×C4×C137—21no—
184C22×C4×C137—21no—
185C22×C4×C137—21no—
186C22×C4×C137—21no—
187C22×C4×C137—21no—
188C22×C4×C137—21no—
189C22×C4×C137—21no—
190C22×C4×C137—22no—
191C22×C4×C137—22no—
192C22×C4×C137—44no—
193C22×C4×C137—44no—
194C22×C4×C137—42no—
195C22×C4×C137—44no—
196C22×C4×C137—42no—
197C22×C4×C137—44no—
198C22×C4×C137—42no—
199C22×C4×C137—42no—
200C22×C4×C137—42no—
201C22×C4×C137—42no—
202C22×C4×C137—42no—
203C22×C4×C137—42no—
204C22×C4×C137C2×D411yescharacteristic
205C22×C4×C137C2×D411yescharacteristic
206C22×C4×C137C2×D411yescharacteristic
207C22×C4×C137C2×D412yes—
208C22×C4×C137C2×D412yes—
209C22×C4×C137C2×D412yes—
210C22×C4×C137#4112yes—
211C22×C4×C137#4112yes—
212C22×C4×C137#4112yes—
213C22×C4×C137C2411yescharacteristic
214M16×C137—28no—
215M16×C137—44no—
216C2×C8×C137—22no—
217C2×C8×C137—22no—
218C2×C8×C137—22no—
219C2×C8×C137—22no—
220C2×C8×C137—22no—
221C2×C8×C137C2×D414yes—
222C4⋊C4×C137—24no—
223C4⋊C4×C137—24no—
224C4⋊C4×C137—21no—
225C4⋊C4×C137—21no—
226C4⋊C4×C137—22no—
227C4⋊C4×C137—22no—
228C4⋊C4×C137—22no—
229C4⋊C4×C137—22no—
230C4⋊C4×C137—42no—
231C4⋊C4×C137—42no—
232C4⋊C4×C137C2×D412yes—
233C4⋊C4×C137C2×D412yes—
234C22⋊C4×C137—24no—
235C22⋊C4×C137—24no—
236C22⋊C4×C137—24no—
237C22⋊C4×C137—24no—
238C22⋊C4×C137—24no—
239C22⋊C4×C137—44no—
240C22⋊C4×C137—44no—
241C42×C137—24no—
242C23×C137—21no—
243C23×C137—21no—
244C23×C137—21no—
245C23×C137—21no—
246C23×C137—28no—
247C23×C137—21no—
248C23×C137—21no—
249C23×C137—21no—
250C23×C137—21no—
251C23×C137—21no—
252C23×C137—21no—
253C23×C137—21no—
254C23×C137—21no—
255C23×C137—21no—
256C23×C137—21no—
257C23×C137—21no—
258C23×C137—21no—
259C23×C137—22no—
260C23×C137—44no—
261C23×C137—44no—
262C23×C137—44no—
263C23×C137—44no—
264C23×C137—44no—
265C23×C137—44no—
266C23×C137—41no—
267C23×C137—41no—
268C23×C137—41no—
269C23×C137—41no—
270C23×C137—41no—
271C23×C137—41no—
272C23×C137#12012yes—
273C23×C137#12112yes—
274C23×C137#12312yes—
275C23×C137AGL(1,ℤ/8)12yes—
276C23×C137#13712yes—
277C23×C137C22×D411yescharacteristic
278Q8×C137—22no—
279Q8×C137—22no—
280Q8×C137—41no—
281Q8×C137—41no—
282D4×C137—22no—
283D4×C137—22no—
284D4×C137—48no—
285D4×C137—48no—
286D4×C137—48no—
287D4×C137—41no—
288D4×C137—41no—
289C2×C4×C137—22no—
290C2×C4×C137—22no—
291C2×C4×C137—21no—
292C2×C4×C137—21no—
293C2×C4×C137—22no—
294C2×C4×C137—21no—
295C2×C4×C137—21no—
296C2×C4×C137—21no—
297C2×C4×C137—21no—
298C2×C4×C137—41no—
299C2×C4×C137—41no—
300C2×C4×C137—41no—
301C2×C4×C137—41no—
302C2×C4×C137—41no—
303C2×C4×C137—41no—
304C2×C4×C137—44no—
305C2×C4×C137—41no—
306C2×C4×C137—41no—
307C2×C4×C137—41no—
308C2×C4×C137—41no—
309C2×C4×C137—41no—
310C2×C4×C137—41no—
311C2×C4×C137—41no—
312C2×C4×C137—41no—
313C2×C4×C137—44no—
314C2×C4×C137—44no—
315C2×C4×C137—48no—
316C2×C4×C137—42no—
317C2×C4×C137—42no—
318C2×C4×C137—42no—
319C2×C4×C137—42no—
320C2×C4×C137—42no—
321C2×C4×C137—42no—
322C2×C4×C137—84no—
323C2×C4×C137—84no—
324C2×C4×C137#12012yes—
325C2×C4×C137#12114yes—
326C2×C4×C137#12114yes—
327C2×C4×C137#12112yes—
328C2×C4×C137#12314yes—
329C2×C4×C137#12312yes—
330C2×C4×C137#12414yes—
331C2×C4×C137C22×D411yescharacteristic
332C2×C4×C137C22×D411yescharacteristic
333C2×C4×C137C22×D411yescharacteristic
334C2×C4×C137C2×#4111yescharacteristic
335C2×C4×C137C2×#4111yescharacteristic
336C2×C4×C137C2×#4111yescharacteristic
337C8×C137—24no—
338C8×C137—42no—
339C22×C137—22no—
340C22×C137—22no—
341C22×C137—22no—
342C22×C137—22no—
343C22×C137—22no—
344C22×C137—22no—
345C22×C137—22no—
346C22×C137—22no—
347C22×C137—22no—
348C22×C137—22no—
349C22×C137—22no—
350C22×C137—22no—
351C22×C137—416no—
352C22×C137—41no—
353C22×C137—41no—
354C22×C137—41no—
355C22×C137—41no—
356C22×C137—41no—
357C22×C137—41no—
358C22×C137—41no—
359C22×C137—41no—
360C22×C137—42no—
361C22×C137—42no—
362C22×C137—42no—
363C22×C137—81no—
364C22×C137—81no—
365C22×C137—81no—
366C22×C137—81no—
367C22×C137#39414yes—
368C22×C137C2×#12011yescharacteristic
369C22×C137C2×#12111yescharacteristic
370C22×C137C2×#12311yescharacteristic
371C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C137C2×#13711yescharacteristic
373C22×C137#57511yescharacteristic
374C22×C137#57511yescharacteristic
375C4×C137—41no—
376C4×C137—41no—
377C4×C137—42no—
378C4×C137—42no—
379C4×C137—42no—
380C4×C137—82no—
381C4×C137—82no—
382C4×C137#39414yes—
383C4×C137C2×#12111yescharacteristic
384C4×C137C2×#12111yescharacteristic
385C4×C137C2×#12311yescharacteristic
386C4×C137C2×#12411yescharacteristic
387C2×C137—24no—
388C2×C137—42no—
389C2×C137—42no—
390C2×C137—82no—
391C2×C137C2×#39411yescharacteristic
392C2×C137#300611yescharacteristic
393C2×C137#300711yescharacteristic
394C2×C137#305511yescharacteristic
395C2×C137#305611yescharacteristic
396C2×C137#309211yescharacteristic
397C2×C137#309311yescharacteristic
398#23482C13711yesmaximal, characteristic, direct product factor, Sylow
399C137#2348211yescharacteristic, direct product factor, Sylow
400C2×#525C2×C13711yescharacteristic
401C2×#428C2×C13711yescharacteristic, complemented
402C2×#417C2×C13711yescharacteristic, complemented
403C2×#417C2×C13711yescharacteristic, complemented
404C2×#407C2×C13711yescharacteristic, complemented
405C2×#380C2×C13711yescharacteristic, complemented
406#2036C2×C13712yescomplemented
407#2035C2×C13712yescomplemented
408#2034C2×C13712yescomplemented
409#2033C2×C13712yescomplemented
410#1736C2×C13711yescharacteristic, complemented
411C22×#41C22×C13711yescharacteristic
412C24×C4C22×C13711yescharacteristic
413C22×M16C22×C13711yescharacteristic
414C22×M16C22×C13711yescharacteristic
415#525—24no—
416#525—24no—
417C2×#123—21no—
418C2×C22⋊Q8C22×C13711yescharacteristic
419C2×C22⋊Q8C22×C13711yescharacteristic
420C2×#121C22×C13711yescharacteristic
421C2×#121C22×C13711yescharacteristic
422C2×#120—21no—
423C2×C4×D4—21no—
424C2×C4×D4—21no—
425C2×#117C22×C13711yescharacteristic
426C22×C4⋊C4C22×C13711yescharacteristic
427C22×C4⋊C4C22×C13711yescharacteristic
428C22×C22⋊C4—21no—
429#428—24no—
430C2×#107C22×C13712yescomplemented
431C2×#106C22×C13712yescomplemented
432#417—24no—
433#417—24no—
434C2×#103C22×C13712yescomplemented
435C2×#103C22×C13712yescomplemented
436C2×#102C22×C13712yescomplemented
437C2×#102C22×C13712yescomplemented
438#407—24no—
439C2×C22⋊C8C22×C13712yes—
440C2×C22⋊C8C22×C13712yes—
441#380—21no—
442#380—21no—
443#380C22×C13712yes—
444#380C22×C13712yes—
445C2×#95—21no—
446#340C22×C13712yescomplemented
447#340C22×C13712yescomplemented
448C25D4×C13711yescharacteristic
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41D4×C13714yes—
455C22×Q8C23×C13711yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C23×C13711yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4D4×C13711yescharacteristic
470C23×C4D4×C13711yescharacteristic
471C23×C4D4×C13711yescharacteristic
472C23×C4C23×C13711yescharacteristic
473C23×C4C23×C13711yescharacteristic
474C23×C4C23×C13711yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16D4×C13714yescomplemented
481C22×C8C23×C13712yes—
482C22×C8C23×C13712yes—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117D4×C13714yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C13712yes—
506C2×C4⋊C4C23×C13712yes—
507C2×C4⋊C4C23×C13711yescharacteristic
508C2×C4⋊C4C23×C13711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—44no—
517C2×C42—21no—
518#107—24no—
519#106—24no—
520#103—24no—
521#103—24no—
522#102—24no—
523#102—24no—
524C22⋊C8—24no—
525C22⋊C8—24no—
526#95—22no—
527#95—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—41no—
535C24—41no—
536C24C2×D4×C13711yescharacteristic
537C24C2×D4×C13711yescharacteristic
538C24C2×D4×C13711yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×D4×C13712yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×D4×C13712yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C13711yescharacteristic
604C22×C4C2×D4×C13711yescharacteristic
605C22×C4C2×D4×C13711yescharacteristic
606C22×C4C2×D4×C13712yes—
607C22×C4C2×D4×C13712yes—
608C22×C4C2×D4×C13712yes—
609C22×C4#41×C13712yes—
610C22×C4#41×C13712yes—
611C22×C4#41×C13712yes—
612C22×C4C24×C13711yescharacteristic
613M16—28no—
614M16—44no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C2×D4×C13714yes—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4C2×D4×C13712yes—
632C4⋊C4C2×D4×C13712yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#120×C13712yes—
672C23#121×C13712yes—
673C23#123×C13712yes—
674C23AGL(1,ℤ/8)×C13712yes—
675C23#137×C13712yes—
676C23C22×D4×C13711yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—48no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4#120×C13712yes—
724C2×C4#121×C13712yes—
725C2×C4#121×C13714yes—
726C2×C4#121×C13714yes—
727C2×C4#123×C13712yes—
728C2×C4#123×C13714yes—
729C2×C4#124×C13714yes—
730C2×C4C22×D4×C13711yescharacteristic
731C2×C4C22×D4×C13711yescharacteristic
732C2×C4C22×D4×C13711yescharacteristic
733C2×C4C2×#41×C13711yescharacteristic
734C2×C4C2×#41×C13711yescharacteristic
735C2×C4C2×#41×C13711yescharacteristic
736C8—24no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#394×C13714yes—
767C22C2×#120×C13711yescharacteristic
768C22C2×#121×C13711yescharacteristic
769C22C2×#123×C13711yescharacteristic
770C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
771C22C2×#137×C13711yescharacteristic
772C22#575×C13711yescharacteristic
773C22#575×C13711yescharacteristic
774C4—41no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—82no—
780C4—82no—
781C4#394×C13714yes—
782C4C2×#121×C13711yescharacteristic
783C4C2×#121×C13711yescharacteristic
784C4C2×#123×C13711yescharacteristic
785C4C2×#124×C13711yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#394×C13711yescharacteristic
791C2#3006×C13711yescharacteristic
792C2#3007×C13711yescharacteristic
793C2#3055×C13711yescharacteristic
794C2#3056×C13711yescharacteristic
795C2#3092×C13711yescharacteristic
796C2#3093×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC2×#525×C137C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C24×C4×C137 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#428×C137C2semidirect
3. C2×#417×C137C2semidirect
4. C2×#417×C137C2semidirect
5. C2×#407×C137C2semidirect
6. C2×#380×C137C2semidirect
7. #2036×C137C2semidirect
8. #2035×C137C2semidirect
9. #2034×C137C2semidirect
10. #2033×C137C2semidirect
11. #1736×C137C2semidirect
31. C2×#107×C137C22semidirect
32. C2×#106×C137C22semidirect
35. C2×#103×C137C22semidirect
36. C2×#103×C137C22semidirect
37. C2×#102×C137C22semidirect
38. C2×#102×C137C22semidirect
47. #340×C137C22semidirect
48. #340×C137C22semidirect
81. C2×M16×C137D4semidirect
398. #23482C137direct (N × H)
399. C137#23482direct (N × H)
401. C2×#428C2×C137semidirect
402. C2×#417C2×C137semidirect
403. C2×#417C2×C137semidirect
404. C2×#407C2×C137semidirect
405. C2×#380C2×C137semidirect
406. #2036C2×C137semidirect
407. #2035C2×C137semidirect
408. #2034C2×C137semidirect
409. #2033C2×C137semidirect
410. #1736C2×C137semidirect
430. C2×#107C22×C137semidirect
431. C2×#106C22×C137semidirect
434. C2×#103C22×C137semidirect
435. C2×#103C22×C137semidirect
436. C2×#102C22×C137semidirect
437. C2×#102C22×C137semidirect
446. #340C22×C137semidirect
447. #340C22×C137semidirect
480. C2×M16D4×C137semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#525×C1372
C2×#428×C1372
C2×#417×C1372
C2×#407×C1372
C2×#380×C1372
#2036×C1372
#2035×C1372
#2034×C1372
#2033×C1372
#1736×C1372
#23482137